On super local antimagic total edge coloring of some wheel related graphs

Abstract

Let G be a connected graph, let V(G) be the vertex set of graph G, and let E(G) be the edge set of graph G. Thus, the bijective function f : V(G) ∪ E(G) −→ {1, 2, 3, …, |V(G)| + |E(G)|} is called a local antimagic total edge labeling if for two adjacent edges e1 and e2, wt (e1) ≠ wt (e2), where for e = uv ∈ G, wt (e) = f (u) + f (v) + f (uv). Thus, the local antimagic total edge labeling by induces a proper edge coloring of a graph G if each edge e is assigned the color wt (e). The local antimagic total edge coloring, denoted by γleat (G) is the minimum number of colors taken over all colorings induced by local antimagic total edge labelings of a graph G. In this research, we determine the local super antimagic total edge coloring of some wheel related graph including fan, wheel, gear and friendship graph.